Diffusion Coding Photography
for Extended Depth of Field
SIGGRAPH 2010
Ollie Cossairt, Changyin Zhou, Shree NayarColumbia University
Conventional Camera (F/1.8)
Focused Image PSF Image Noise Captured Image
Camera Blur ModelSpati
al dom
ain
Focused Image MTF Image Noise Captured ImageFrequency
dom
ain
Deblurring Problems
MTFCaptured image
Low SNR
low MTF values
Problem 1:
Focused image
Lens
Sensor
P
Object
Q
Problem 2:
Variation with depth
Extending Depth of Field: Previous Work
Focus Sweep Cameras[Hausler ’72]
[Nagahara et al. ’08]Lens Focal PlaneSensor
Wavefront Coding Cameras
[Dowski and Cathey ’95] [Chi and George ’01] [Garcia-Guerrero et al. ‘07]
Other Related Work[Levin et al. ’07][Veeraraghavan et al. ’07] [Levin et al. ’09]
Focus Sweep Camera
Lens
Scene
Sensor
+ + + + + + =InstantaneousPSF
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7
Final PSF
[Hausler ’72][Nagahara et al. ’08]
Focus Sweep Camera
+ + + + + + =InstantaneousPSF
t = 1 t = 2 t = 3 t = 4 t = 5 t = 6 t = 7
Final PSF
InstantaneousPSF
t = 1
+
t = 2
+
t = 3
+
t = 4 t = 5
+
t = 6
+
t = 7
+
depth
1depth
2
[Levin et al. ’09]
2D MTF
=
Final PSF
Lens
Scene
Sensor
[Hausler ’72][Nagahara et al. ’08]
Wavefront Coding
Lens Scene
Sensor
[Levin et al. ’09]
2D MTF
Cubic Phase Plate
x u
[Dowski and Cathey ’95]
y
Ambiguity Function
slice
MTF
Lens Resolution Target
Sensor
Focu
s S
weep
Wavefr
on
tC
od
ing
EDOF Camera Comparison
depth
Focu
s S
weep
Wavefr
on
tC
od
ing
Deblurred image
EDOF Camera Comparison
Deblurring Error vs. Depth
Deblu
rrin
g E
rror
noise
Deblurring Error
Deblurring Error
Depth
Wavefront Coding
Focus Sweep
Focus Sweep Wavefront Coding
Is it possible to achieve the performance of focus sweep
without moving parts?
Optical DiffusersCircular diffuser
[http://www.luminitco.com]
Diffuser sheets
w
SensorDiffuser
Light ray
x
x
Scatter function
w
SEM image
Diffuser Kernels
LensSensor
x u
A
u
x
A/2
-A/2
With diffuser
A/2
-A/2
u
x
Without diffuser
Light
field
space
w w
A/2
-A/2
u
x
Without diffuser
Diffuser Kernels
LensSensor
w
u
x
With diffuser
w
Light
field
space
x u
Diffuser Kernels
LensSensor
w
u
x
A/2
-A/2
u
x
u
x
Diffuser kernel
Light field Diffuser kernel
Coded light field
x u
Without diffuser With diffuser
Light
field
space
Diffusion Coded PSF
A/2
-A/2
u
x
Without diffuser
u
x
With diffuser
u
x
Diffuser kernel
x
project
x
project
Light
field
space
x
project
Senso
r sp
ace
Camera PSF Scatter function
Coded PSF
Radially Symmetric Light Field
Lensv
u
Sensor
For an on-axis, isotropic point source:
Radially Symmetric Diffuser
For a radially-symmetric diffuser kernel
Lens Sensor Sensor
Radially Symmetric Diffuser PSFs
Radially symmetric diffuser
Coded PSF Scatter function
Camera PSFCoded PSF Scatter function
Camera PSF
Conventional diffuser
Normalized frequencyNormalized frequencyNormalized frequencyNormalized frequency
PSF Vs. Depth
MTF Vs. Depth
k7
k9
k11
k13
K7
K9
K11
K13
-50px 50px -50px 50px -50px 50px -50px 50px
depth
depth
Diffusion Coding Performance
Deblurring Error vs. Depth
Depth
Wavefront CodingFocus Sweep
noise
Diffusion Coding (light field)Diffusion Coding (wave optics)
Similar performance to focus sweep without moving parts
Diffuser ImplementationDiffuser scatter function
)(rf
r (mm)110
Th
ickn
ess
(u
m)
3
863
2
1
)(rt
r (mm)
[www.rpcphotonics.com]
Diffuser heightmap Fabricated Diffuser
Diffuser surface profile
[Sales et al. ‘03]
Garcia-Guerrero
Comparison with Prior Work
Deblurring Error vs. Depth
Depth
Diffusion Coding
Diffusion coding significantly outperforms prior work
Diffusion Coding Experiments
Fabricated DiffuserCannon 50mm EF lensCannon 450D Sensor
Experimental Setup
Measured PSFs
depth
Without diffuser
with diffuser
BM3D Deblurring Algorithm
[Dabov et al. ‘08]
Examples
Conventional Camera
f-number = 1.8, exposure time = 16ms
Conventional Camera
f-number = 18 , exposure time = 16ms
Diffusion Coding
Captured
f-number = 1.8, exposure time = 16ms
Diffusion Coding
Deblurred
f-number = 1.8, exposure time = 16ms
Conventional Camera
• f-number = 1.8• exposure time = 10ms
Diffusion Coding
• f-number = 1.8• exposure time = 10ms
Captured
Diffusion Coding
• f-number = 1.8• exposure time = 10ms
Deblurred
Conventional Camera
• f-number = 1.8• exposure time =
12.5ms
Diffusion Coding
• f-number = 1.8• exposure time =
12.5ms
Captured
Diffusion Coding
• f-number = 1.8• exposure time =
12.5ms
Deblurred
Conventional Camera
f-number = 1.8, exposure time = 16ms
Diffusion Coding
Captured
f-number = 1.8, exposure time = 16ms
Diffusion Coding
Deblurred
f-number = 1.8, exposure time = 16ms
LimitationsConventional Camera Diffusion Coding
•Loss of image texture
•Loss of contrast
•Occlusion errors
Conclusions
Diffusion Coding Theory
Diffusion Coding Examples
Radially Symmetric Diffusers
LensSensor
Diffuser
Diffusion Coding Implementation
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